In our experience, given an FDN reverberator structure, setting the delay
lengths can be a rather tedious job. The vast majority of possible delays
just provide poor results in the sense that the time response is too
``rough'' or the frequency response is too ``colored.'' An interesting
approach to this problem might be to use nonlinear optimization techniques
such as ``simulated annealing'' or ``genetic algorithms'' to optimize the
delay lengths such that ``perceptual uniformity'' of the response is
maximized in the time and frequency domains jointly.

Designing the delay lengths from room geometry has the property of giving a
reverberator which is always consistent with a desired room in that the
low-frequency modes are matched. However, there does not seem to be any
compelling reason to match specific low-frequency mode tunings. Noticeable
room resonances are normally perceived as defects in a listening space.
Early reflections, on the other hand, contribute strongly to the perceived
``spatial impression'' [2]. In other applications, however,
such as modeling the soundboard of a piano as a reverberator, the specific
coloring or ``equalization'' provided by the reverberator is important and
must be preserved. In such applications, it is normally necessary to match
low-frequency resonances accurately and high-frequency resonances only
statistically.

When the FDN order is large (larger than 8 for satisfactory results), poor
results can still be obtained when modeling desired room dimensions which
are not favorable. In fact, even for the shoe-box room shape, the relative
dimensions play a very important role in determining the smoothness of the
reverb [15]. Of course, diffusion contributes
significant smoothing to the response, so full feedback matrices (as
opposed to diagonal feedback matrices) are especially needed to achieve
good reverberators using low-order FDNs.

On balance, it seems that what is needed for good reverberator design in
general is

(1)

precise matching of early reflections,

(2)

minimal coloration due to uneven mode distributions in the frequency domain,

smooth, rich echo density late in the impulse response,
having no noticeable patterns.

These desiderata indicate that, rather than attempting to model
real rooms, lossless prototype FDNs optimizing criteria (2) and (4) should
be found, for a given order, which have at least one delay line long enough
to support injection of specific early reflections to satisfy (1), and then
lowpass filters as in (21) should be added to satisty criterion (3).
The main open issue is how the optimization of (2) and (4) should best
be carried out for specific classes of structurally lossless feedback
matrices.